Transient response of magnetorheological fluid on rapid change of magnetic field in shear mode

The transient behaviour of magnetorheological (MR) devices is an important parameter for modern semi-actively controlled suspension systems. A significant part of the MR device response time is the MR fluid response time itself. A significant factor is the so-called rheological response time. The rheological response time is connected with the structuring particle's time and the development of shear stress in MR fluid during the deformation. The main aim of this paper is to experimentally determine the rheological response time of MR fluid and evaluated the effect of shear rate, magnetic field level, and carrier fluid viscosity. The unique design of the rheometer, which allows the rapid change of a magnetic field, is presented. The rheological response time of MRF 132-DG and MRC-C1L is in the range of 0.8–1.4 ms, depending on the shear rate. The higher the shear rate, the shorter the response time. It can be stated that the higher the magnetization of the MR fluid, the lower the response time. The higher the viscosity, the higher the rheological response time. The measured data of rheological response time was generalized and one master curve was determined.

www.nature.com/scientificreports/ The research studies of Sherman 14 or Goldasz et al. 15 show that MR valve pressure drop due to MR fluid yield stress decreases with the increasing gap velocity. At high velocities, this pressure drop is approaching to be zero. This statement is based on CFD (computational fluid dynamics) simulations. This phenomenon is related to transient rheology connected with the development of the velocity profile in the gap and is often referred to as the hydrodynamic fluid response time. Goncalves et al. 16 experimentally determined that the hydrodynamic response time is 0.73 ms for magnetic field 100 kA/m and 0.53 ms for magnetic field 200 kA/m. The commercial MRF-132LD (Lord Corp., USA) was used in this study. Kubík et al. 17 published similar study. This team measured the hydrodynamic response time of MR fluid MRF-132DG (Lord Corp., USA) and ranges from 0.4 to 1 ms for a selected gap size and a range of magnetic field stimuli. The velocity profile development mechanism is similar for MR fluid and electrorheological (ER) fluid 18 . However, ER fluid show faster response time than MR valve. ER fluid is the suspension of fine electrically active particles in fluid. This fluid exhibits a rapid increase of fluid yield stress under the application of an electric field. Gavin et al. 19 modelled the transition from a fully developed Bingham profile to a Newtonian flow for ER fluid. The yield stress of ER fluid was assumed to drop to zero quicker than the dissipation energy due to the development of the velocity profile 19 . It can be stated that this hydrodynamic response time is connected with high shear rates or fast changes of the magnetic field in valve mode.
The particle structure development response time is related to the time needed for the structuring of particles in the direction of the magnetic field without the flow conditions of the MR fluid. Jolly et al. 20 proposed an experimental method that microstructure formation time can be deduced from the transient changes in the relative magnetic permeability of the MR fluid. The chained particles are assumed to have a higher magnetic permeability than the dispersed. Two-time responses were observed 20 . The first attributes the connection with the transfer of particles into diverse chains (pair formation) and the second (an order of magnitude slower) connection with the migration of these initial chains into longer and stronger structures. The response time was between 5 and 10 ms. A similar measurement method was also published by Horváth et al. 21 . Pei et al. 22 stated that the response time of dry MR fluid was in the order of µs by the model. This statement is based on simulation results.
The rheological response time is connected with the structuring particle's time and the development of shear stress in MR fluid during the deformation (flow). Sherman et al. 23 create a chain model of MR fluid. This model is based on one million particles. One result of this paper is the shear stress time history on the step change of a magnetic field. For this data, the rheological response time can be determined as roughly 0.4 ms. The MR fluid had a volume particle fraction of 25% and was under the shear rate of 500 s −1 . Laun and Gabriel 24 determined the response time of MR fluid of 2.8 ms. They used sinusoidal excitation and the determined time lag between magnetic flux density and shear stress. Kikuchi et al. 25 examined the response time to a step electric current and introduce non-dimensional response time parameter. It can be expected that the mechanism of chain formation in Electro-rheological (ER) fluids and MR fluids is similar. Koyanagi et al. 26 developed a method for a measurement response time of ER fluid. This team experimentally determined the response time as 0.95 ms.
The information about the transient behaviour of MR fluid is limited. This issue is becoming more important due to the development of MR devices with a short response time 7,27 , where the limiting part is now the MR fluid itself. The current design of the MR damper achieved a response time of about 1.2 ms. In the current state of the art, more studies can be found dealing with the response time of MR fluid 7,12 than is presented above. In these several cases, the authors measured the time constant of measuring devices instead of the time constant of MR fluid 14 . The rheological response time of MR or ER fluid was just experimentally determined in studies 24,26 . Both studies presented response time just for one experimental condition. The main aim of our paper is to experimentally determine the rheological response time of MR fluid and evaluated the effect of shear rate, magnetic field level, and carrier fluid viscosity. Our results will be compared with the published analytical approach 14 .

Materials and methods
Description of the measured phenomenon and measuring methods. The aim of the measurement is to experimentally determine the time constant of MR fluid in the shear mode (from the increase in shear stress τ) on a rapid change in the magnetic field B. The procedure of the experiment is described in Fig. 1. At time T 1 , the MR fluid is loaded by given shear rates and the magnetic field is off. At time 0, the magnetic field is activated and, at time T 2 , the magnetic field is already at the maximum value. However, until time T 3 , the shear stress remains at the same level as at time T 1 . In the author's opinion, this delay is associated with particle structure formation in the MR fluid. In reality, there are no separate single chains. That is just a tentative simplification. At time T 4 , there is a rapid increase in shear stress in the MR fluid due to the deformation of the particle structure. This is shown as tilting chains in the shear direction but the mechanisms of structure fracture are more complex. Generally, the simplest dynamic system, that can serve as an approximation of the transient behavior of MR fluid is a first-order system. The transient response is expressed by the time constant T 63 (primary response time), which determines the time when monitored torque (calculated shear stress) achieved 63.2% of the final controlled value (steady-state). This approximation can be used for the description of the dynamic behaviour of MR actuators 28 . In the case of rheology measurement, the MR fluid can be described by a simple Maxwell model and by Bingham constitutive equation. For step change on magnetic field, the excepted shear stress response τ(t) would be: where t is time. More names for a variable T 63 can be found in the literature as switching time 24 , response time 17 or rheological response time 14 . However, the transient response of MR fluid exhibits different behaviour than the first-order system, see Fig. 5. Therefore, we decided to determine those time constants in our paper: (1) firstorder time constant T 63 (0-63.2%) and (2) (2) inductance of the rheometer electromagnetic coil 7 . In our rheometer, we used soft magnetic composite (SMC) material (trademark Sintex) for the magnetic circuit to eliminate eddy currents. SMC material is magnetic conductive and electric non-conductive (resistivity 280 µΩm). The suitable design of a magnetic circuit with our patented current controller allows a rapid increase of electric current on the electromagnetic coil (T 63I = 0.21 ms).
Methodology measurement. The aim of the experiments was to determine shear stress in MR fluid and magnetic field over time. The shear stress τ was calculated from area and torque which was measured indirectly based on data from the force sensor (MEG20) on the lever, see Fig. 2. The force sensor measuring range was 0-200 N. The force range (deformation) was chosen to maximize system rigidity and only the first 10% of the range was used for measurement. The magnetic field in the gap corresponds with the electric current course and was measured by Fluke i30 current clamps. These two signals were recorded and conditioned with a sampling frequency of 200 kHz by the Dewetron USB-50 analyzer. The MFG-2120MA signal generator generates a square wave voltage signal which inputs to the current controller at a frequency of 1 Hz. Our developed current controller generates an electric current on the electromagnetic coil with over-voltage up to 100 V. The measurement procedure was as follows: (1) 10 s measurement without magnetic field, and (2) 10 s measurement with the application of the magnetic field. This procedure was necessary for the elimination of non-constant friction forces in the rheometer and viscous forces. Those phenomena can significantly complicate the subsequent evaluation of response time. The experiments were conducted 5 times under the same conditions. The data was not filtered but averaged from raw data. Then, the ramp data was normalized. All measurements were performed at 25 °C ± 1 °C.
Methodology evaluation of response time. The measured response time of the magnetic field (electric current) achieved a value of τ 63I = 0.21 ms and τ 90I = 0.33 ms, see Fig. 4. In several cases of the transient behaviour of MR actuators, this time can be expected as a step change. In our case, we cannot make this simplification because the expected response time of MR fluid from published models 14 is in the same time scale (roughly 1.5 ms). Therefore, it was necessary to determine the transfer function between the measured magnetic field and shear stress in MR fluid. We used a process model for describing the MR fluid transient response. The process www.nature.com/scientificreports/ model is popular for describing system dynamics in many industrial applications 29 . We used the so-called simple SISO (Single Input, Single Output) process model which is described by this transfer function: where K p is the proportional gain, T p is the time constant, and T d is dead time. A similar approach was used in study 26 . The Matlab System identification toolbox was used for the identification of constants. The length of the evaluated section was 20 ms.  Table 1. These fluids were chosen because they have a similar particle size and a different viscosity of the carrier fluid. The viscosity listed in the table was measured by the Haake Rotovisco 1 rheometer, and determined as a slope between 400 and 800 s −1 . It should be noted that carrier fluid of MR fluids exhibits Newtonian behaviour but MR  www.nature.com/scientificreports/ fluids are in general non-Newtonian. The particle sizes were measured by a scanning electron microscope, FEG SEM ZEISS Ultra Plus, and analysed by script using tools for picture analysis in Matlab. However, the information about particle size of MRC-C1L was taken from study 30 . Control electric current signal. First of all, it was necessary to precisely describe the excitation of MR fluid. It can be assumed that the course of magnetic flux density in the MR fluid copies the course of an electric current due to the elimination of eddy current in the magnetic circuit. This is ensured by a special design of the rheometer. The course of the electric current I in time t can be seen in Fig. 4 for two levels of electric current  where γ is shear rate. The Non-dimensional response time T * and Mason number M n were calculated from measured data, see Fig. 7. The master curve can be determined from measured data, see Fig. 7-red line. The results show a significant difference between the published model 14 and our experiment for M n values higher than 0.005. The T * and M n was also evaluated (estimated) from papers 24,26 . This data is out of range of our measurement. However, it should be noted that the data obtained from the experiment are only from study 24 . The difference in the results may be due to (1) the model simplification and (2) inaccuracies in the measurement and evaluation of the measured data. It has been hypothesized that the difference may be due to the deformation of the measuring device (rheometer), which is not included in the model. This would result in a significant increase in response time T 90 at low shear rates γ compared to the model. Figure 8 shows a comparison of the response time T 90 course on shear rate γ from the Sherman model, proposed model (Fig. 7 red) and from the experiment for MRHCCS4-B. The carrier fluid viscosity η , magnetization M, shear rates γ are the same for experiments and also for the model. It can be seen that the response time T 90 from experiments is significantly lower than that from the model. Thus, it can be stated that the possible deformation of the measuring device is not the source of the difference between the experiment and the model. The difference can be explained by certain simplifications of the model. However, both curves have an exponential www.nature.com/scientificreports/ character and therefore the model describes trends very well. Another significant difference is that measured MR fluid contains additives that are not included in the model. The question is how significant a difference can create this simplification. The surface roughness can also affect MR fluid dynamics 33 . This is also not included in the model, and can also play an important role.

Conclusion
This paper deals with the experimental determination of magnetorheological fluid transient response (rheological response time) on the rapid change of a magnetic field in shear load mode. A unique rheometer was presented that allows almost unit step of magnetic fields and also allows the measuring of the development of MR fluid shear stress over time. The transient response was determined on four MR fluids that differ in supplier, particle concentration, or carrier fluid viscosity. The paper also includes a magnetic model and its experimental verification. The most important conclusions of the paper are the following: • The response time of the magnetic field is T 90I = 0.335 ms and slightly increases with an increasing maximum value of electric current. • The rise of shear stress exhibits an initial dead time of 0.4 ms, which is independent of the shear rate level.
• The value of the shear rate significantly influences the rheological response time at low shear rates. The higher the shear rate, the shorter the response time. The measured data of the response time can be fitted by a power-law function. The response time T 90 ranges from 5.5 to 1.9 ms for shear rate γ from 11 to 218 s −1 for MR fluid MRHCCS4-A and MRHCCS4-B.   www.nature.com/scientificreports/ • All measured data was generalized in the term of non-dimensional response time T * and Mason number M n . One master curve (T* = 4.1939M n −0.35 ) can be determined from measured data independent of magnetization M, carrier fluid viscosity η , shear rates γ , etc. This is an important conclusion because the master curve allows the determination of rheological time response for a given MR fluid and given load (shear rates).
It should be noted that the our experimentally determined master curve shows a deviation from the model 14 . MR fluids used in the experiment and model differ in the type or concentration of additives (the model does not include additives), which may also affect the transient response. For this reason, a plan for further research in this area is to determine the rheological response time for homemade MR fluid (full control of additives) and measurement for a higher range of Mason numbers. We also see the potential for future research in the area of a particle chaining model that allows the showing of particle motion during the step change of a magnetic field.